Algebra 2 Final Exam

Algebra 2 Spring 2025 Final Exam Review #1 Probability and Statistics Name: Answer Key Date: Period: Number: Second Roll 1. Use the table to the right to determine what the probability of each event would be: a) Sum greater then 7 P(>7)= 15/34 b) that is odd 1/psi V_{2}/(VV) P (vdd) = 18/34 c) that is greater than 7 or odd 3/4 P(>7W0)= 15/(3w) + 19/(3w) - w/(3w) = (2f)/(3w) (1.1) (1.2) (1.3) (1,4) (1,5) (1.6) (2.1) (22) (2.3) (2,4) (2.5) (2.6) (3.1) (3.2) (3.3) (3.4) (3,5) (3.6) (4.1) (4.2) (4,3) (4.4) (4.5) (4,6) d) Sum that is greater than 7 and odd P(>7,0)= u/(3w) (5.1) (5,2) (5.3) (5.4) (5.5) (5.6) (6.1) (6.2) (6,3) (6,4) (6,5) (6,6) 2. A marble is selected at random from a jar containing 5 red marbles, 2 yellow marbles, and 6 green marbles. What is the probability that the following occur: a) the marble is red? epsilon_{p}/15 P(R) b) marble is not yellow? P(- Y) = 1 - 2/13 55/(sqrt(2)) c) marble is either red or green? P(KJ4)= 5/13 + 6/13 11/17 3. In a 52-card deck, what is the probability of drawing the following: a) A and then a 2 with replacement: 1/149 P(k cap2)= 4/52 * 4/52 b) An a black card: P(AV8)= 4/(5k) + (2psi)/(5k) - 2/(5k) = 28/52 1/(1 ^ 2) 4. When voters were polled, 73% said they were voting "yes" on an initiative measure, with a margin of error of (plus/minus 5.4)% 7000(0.72 plus/minus 0.054) a) what is the minimum number of voters who voted yes [A] 162 [B] 2028 [C] 2028 [D] 2352 b) what is the maximum number of voters who voted yes [A] 162 [B] 2028 [C] 2028 [D] 2352 5. The table shows differences in political ideology, by education, for a random sample of voters. Liberal Moderate Conservative High School only 19 15 11 College 20 14 21 a) The probability randomly selected person from this group is conservative, given they have attended college: P( Con |Coll) b) The a randomly selected person is from high school given they are moderate: P(HS| Med ) 45/29 6. The table below shows the number of students at a school and the number of student drivers. Student Driver Not a student Driver Total Male 440 720 1160 Female 460 630 1090 Total 900 1350 2250 Determine the probability that a person chosen at random is a student driver given P(\$D|f)= 440/1091 A. P(F| SD )= 23 45 C. P(M| SD )= 22 45 B. P( SD |M)= 11 29 D. P( SD |F)= overline 46 109 7. The local health clinic surveys their patients about their water drinking habits. They find the data is normally distributed showing the mean ounces of water consumed daily is 58 and the standard deviation is 6.1. How many ounces per day do 99.7% of their patients drink? A. 45.8 oz-70.2 oz C. 39.7 oz-70.2 oz B. 39.7 oz-76.3 oz D. 45.8 oz 76.3 oz 743 45.5 58 たたかう 8. A local table leg factory checks every 10th table leg created for defects. This method of sampling is called... A. Systematic C. Self-Selected B. Simple Random D. Stratified 9. Label the blank normal distribution curve below. Be sure to label the mean and the standard deviations. Also include the appropriate percentages given by the empirical rule. 045 2.35/ M-30 M -2 theta^ prime prime 13.51 341 241 13.51 4-0 99.7/ 951 -७8%- M M+9 2.51 M + 2 * theta deg Mr30 0.151. 10. A pharmaceutical company wants to test a new medication and is asking for volunteers to participate. This method of sampling is called... A. Systematic C. Self-Selected B. Cluster D. Stratified 11. A poll is taken for a new city ballot initiative. The city is divided into 10 regions and then 3 of those regions are polled. This method of sampling is called... A. Self-Selected B. Simple Random C. Cluster D. Stratified 12. Housing costs in the Peoria area are exploding. The mean cost of renting a 2-bedroom apartment is $2000 with a standard deviation of $130. What percent of 2-bedroom apartments are between $1740 and $2260? A. 68% B. 84% C. 95% D. 99.7% 1970 200 2130 1610 1740 2100 2300 13. Suppose the scores on a test given to all juniors in a school district are normally distributed with a mean of 72 and a standard deviation of 6. A. Find the percent of juniors whose score is between 66 and 84 34 + 34 +13.5:81.5/. B. Find the probability that a randomly chosen junior has a score below 60 15 + 1.35 =7.5/ C. Find the percent of juniors whose score is between 61 and 75 SKIP D. Find the percent of juniors whose score is greater than 82 SKIP Quadratics Perform the indicated operation: 14. ( 5 - 70 ^ 2 = 75 - 70L * 749L ^ 2 - 24 - 70lambda 16. (- 3 - 2i) - (7 + i) = 10-31 18. Which of the following is a solution: Choose all answers that apply. x ^ 2 - 6x + 18 x ^ 2 - (18x + c) = - 18 + 9 A. 3 + sqrt(3) (x - 3) ^ 2 = - 9 B. 1 - 3l X - 3 = 3L C. 3 + 3i D. - 3 + 3i E. 3 - 3t x = 3 plus/minus 3 * L 15. (7 + 1)(- 6 - 2i) = - 4i - 20i - 2i ^ 2 - 40 - iOL 17. (2 - 5i) + (- 9 + 3i) = -7-20 19. Solve the system of equations. Choose all answers that apply. y=x^ 2 -4\\ 2x + y =4-9x A. Β. (2, 12) C. (4,0) D. (-4,2) Ε. (2,0) x ^ 2 - 4 = 4 - 2x x ^ 2 + 2x - 8 = 0 (x + 4)(x - 2) = 0 x = - 4, 2 y = 1w - 4 y = 4.4/0 20. Find the rate of change f(x) = x ^ 2 + 12x + 32 Over the interval [1,4] A. 3/51 11 12 32 4113 B. 51/3 113 45 C. 45/96 D. 96/45 4/1 12 32 110 96 (9y - 45)/(4 - 1) = 51/3 22. Given that the functions fand g are defined by f(x) = x ^ 2 - 2x and Evaluate: g(3) = 9 - 5 g(x) = 3x - 5 f(g(3)) = (4) ^ 2 - 2(4) = 16 - 8 f(x) - 3g(x) = x ^ 2 - 2x - (9x - 15) x ^ 2 - 11x + 15 f(x) + g(x) = X ^ 2 - gamma*X + 3X - 5 21. How many unique real solutions Does the system have? y = x ^ 2 - 3x - 7; y = x - 3 X ^ 2 - 3X - 7 = X - 3 x ^ 2 - 4x - 4 = 0 (- 4) ^ 2 - 4(1)(- 44) B. 2 A. 1 10+10 C. 0 3270 D. Infinitely many 23. Solve: - 4x + 12x ^ 2 = - 6 A. x = (1 plus/minus l * sqrt(17))/6 17x ^ 2 - 4x + v = 0 2(10x ^ 2 - 2x + 3) = 0 B. x = (- 7 plus/minus sqrt(769))/18 x = (2 plus/minus sqrt(4 - 4(18)))/12 2108 C. x = (7 plus/minus sqrt(769))/18 (2 plus/minus sqrt(- 48))/12 X ^ 2 + X - 5 D. x = (- 2 plus/minus i * sqrt(15))/6 (2 plus/minus 2 * i * sqrt(17))/12 24. Find the parts of the quadratic function: f(x) = x ^ 2 - 3x + 12 Vertex: (3/4, 29/4) (Min or Max) WHIC 4 Axis of symmetry: x = 3/2 x-intercepts: Nit Real Domain: (0, ∞) Range: [34/4, 0) f(3/2) = (3/2) ^ 2 - 3(3/2) + 1psi q/4 - q/2 + 10 X = (- (- 3))/(2(1)) = 3/2 49/4 - 18/4 + 41/4 37/4 25. Jason jumped off a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function h(t) = - 16t ^ 2 + 16t + 480 where t is the time in seconds and h is the height in feet. At what height will Jason reach his maximum height? What time will that be at? y = - 10(1/2) + I * 0(1/2) + 48 X = (- psi)/(2(- psi)) = (- psi)/- 32 = 1/2 - 4 + 8 + 4 * 0 at 0.5 seconds t max heighit 15 484 ft Polynomial equations 26. Find the maxima and minima of the graph max: (- 1/2, 1) mm: (2,-4) max value min value: 27. What are the turning points of the following functions: f(x) = - x ^ 4 - 5x ^ 3 + 2x ^ 2 + 6x *graph find x-valves of Max/min max: (39,72.3) (0.70, 3.23) Min (0.95,-1.95) Find all zeros. 28. y = 3x ^ 4 + 4x ^ 3 + x ^ 2 A. x =0(mult.of 2),-2,- 1 3 B. x =0(mult.of 2),-1,- 1 2 C. x =0(mult of 2),-1(mult,of 2) D. x =0(mult.of 2),-1,- 1 3 x ^ 2 * (2x ^ 2 + 4x + 1) x ^ 2 * (3x + 1)(x + 1) x = D_{1} - 1/3 - 1 29. f(x) = - x ^ 3 + 5x ^ 2 + 6x - x * (x ^ 2 - 5x - 4) - x * (x - 6)(x + 1) x = - 1, 0, 6 A. x = - 6, 0, 1 B. x = - 6, - 1, 0 C. x = - 1, 0, 6 D. x = 0, 1, 6 Choose a correct factor for each of the following polynomials. 30. 4x ^ 3 - 32 4(x - 2)(x ^ 2 + 2x + 4) 4(x ^ 3 - 8) A. (2x + 16) B. (x - 2) C. 4(x ^ 3 - 8) D. (x - 4) 31. 81x ^ 4 - 16 A. (9x + 4) B. (9x - 4) C. ( 3x underline +2) D. (3x + 4) (9x ^ 2 - 4)(9x ^ 2 + 4) (3x - 2)(3x + 2)(9x ^ 2 + 4)